# Stable self-similar blowup for a family of nonlocal transport equations

## TL;DR

This paper demonstrates the existence of stable self-similar blow-up solutions in a family of nonlocal transport equations modeling vortex stretching in fluid dynamics, using advanced modulation techniques.

## Contribution

It introduces a novel application of modulation techniques to establish stable blow-up in nonlocal transport equations related to Euler dynamics.

## Key findings

- Stable self-similar blow-up solutions are constructed.
- The blow-up behavior is shown to be stable under perturbations.
- The results connect nonlocal transport models with classical Euler vortex stretching phenomena.

## Abstract

We consider a family of non-local problems that model the effects of transport and vortex stretching in the incompressible Euler equations. Using modulation techniques, we establish stable self-similar blow-up near a family of known self-similar blow-up solutions.